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大整數(shù)相乘，輸入小數(shù)也可以，其原理是分塊相乘，將輸入的數(shù)對半分成高位和低位，使大整數(shù)劃分為小數(shù)，然后將小數(shù)相乘獲取原高地位的大數(shù)

可以通過規(guī)律:大整數(shù)1*大整數(shù)2=高位1*高位2+中位進位+中位(高位1乘低位2+低位1乘高位2)+低位進位+低位1*低位2

拼接大整數(shù)

java代碼如下:

// 分塊相乘

public?String bigMul(String num1, String num2,?int?len) {

if?(null?== num1 ||?"".equals(num1) ||?null?== num2 ||?""?== num2) {

return?"0";

}

int?pointNum = 0;// 小數(shù)點移位距離

// 如果是小數(shù)

if?(num1.contains(".")) {

pointNum += num1.length()-num1.indexOf(".")-1;

String h = num1.substring(0, num1.indexOf("."));

String l = num1.substring(num1.indexOf(".") + 1);

num1 = h + l;

}

if?(num2.contains(".")) {

pointNum += num2.length()-num2.indexOf(".")-1;

String h = num2.substring(0, num2.indexOf("."));

String l = num2.substring(num2.indexOf(".") + 1);

num2 = h + l;

}

// 取得最長的數(shù)

// 將長度調(diào)整相同

num1 =?formatNumber(num1, len);

num2 =?formatNumber(num2, len);

// 如果長度小于4，則直接乘

if?(num1.length() <= 4) {

String result = String.valueOf(Integer.valueOf(num1)

* Integer.valueOf(num2));

String setPoint = setPoint(pointNum, result);

return?setPoint;

}

// 如果長度大于四，將兩個數(shù)分成高低位

int?halfLen = len / 2;

int?halfLen2 = len - halfLen;

String num1H = num1.substring(0, halfLen);

String num1L = num1.substring(halfLen);

String num2H = num2.substring(0, halfLen);

String num2L = num2.substring(halfLen);

int?maxLen = Math.max(halfLen, halfLen2);

// 高位*高位

String H1H2 = bigMul(num1H, num2H, halfLen);

// 高位*低位

String H1L2 = bigMul(num1H, num2L, maxLen);

// 低位乘高位

String L1H2 = bigMul(num1L, num2H, maxLen);

// 低位*低位

String L1L2 = bigMul(num1L, num2L, halfLen2);

// 從低位開始，先取低位的進位

String[] carryL = getCarry(L1L2, halfLen2);

// 將中間兩位相加

String mid = additionMid(H1L2, L1H2);

String carry = carryL[0];

if?(carry !=?null?&& !carry.equals("0")) {

mid = additionMid(mid, carry);

}

// 首位加上中位進位再取進位

String[] carryMid = getCarry(mid, maxLen);

String carryM = carryMid[0];

String high =?"";

high = additionMid(H1H2, carryM);

// 將三者疊加即可

String result = high + carryMid[1] + carryL[1];

result = setPoint(pointNum, result);

return?result;

}

private?String setPoint(int?pointNum, String result) {

// 設(shè)置小數(shù)點

if?(pointNum > 0) {

String sRes =?"."?+ result.substring(result.length() - pointNum);

String hRes = result.substring(0, result.length() - pointNum);

result = hRes + sRes;

}

return?result;

}

private?String additionMid(String h1l2, String l1h2) {

int?carryFlag = 0;

int?maxLength = Math.max(h1l2.length(), l1h2.length());

h1l2 =?formatNumber(h1l2, maxLength);

l1h2 =?formatNumber(l1h2, maxLength);

String numRes =?"";

String[] result = {?"0", numRes };

for?(int?i = maxLength - 1; i >= 0; i--) {

int?num1 = Integer.parseInt(h1l2.substring(i, i + 1));

int?num2 = Integer.parseInt(l1h2.substring(i, i + 1));

int?singleAddition = num1 + num2 + carryFlag;

carryFlag = 0;

if?(singleAddition >= 10) {

carryFlag = 1;

singleAddition -= 10;

}

numRes = singleAddition + numRes;

}

result[0] = String.valueOf(carryFlag);

result[1] = numRes;

// 如果最高位有進位，則加上去

if?(carryFlag != 0) {

numRes = carryFlag + numRes;

}

return?numRes;

}

// 0:進位,1:值

private?String[] getCarry(String l1l2,?int?len) {

String carry[] = {?"0", l1l2 };

if?(l1l2.length() > len) {

// 有進位

int?sub = -len + l1l2.length();// 獲得多出來的長度

String substring = l1l2.substring(0, sub);// 截取進位長度

String valueString = l1l2.substring(sub);// 截取進位后的長度

carry[0] = substring;

carry[1] = valueString;

}?else?{

for?(int?i = l1l2.length(); i < len; i++) {

carry[1] =?"0"?+ carry[1];

}

}

return?carry;

}

@Test

public?void?fun() {

//首數(shù)字不能為零

String num1 =?"14.4";

String num2 =?"1.42";

String bigMul = bigMul(num1, num2,

Math.max(num1.length(), num2.length()));

bigMul = getPruNum(bigMul);

System.out.println(bigMul);

}

private?String getPruNum(String bigMul) {

for?(int?i = 0; i < bigMul.length(); i++) {

String w = bigMul.substring(0, 1);

if?(w.equals("0")) {

bigMul = bigMul.substring(1);

}?else?{

return?bigMul;

}

}

return?bigMul;

}

轉(zhuǎn)載于:https://my.oschina.net/zhouzhenBlog/blog/648151

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